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Simplifying (r + 5)(r + 5) = 11 Reorder the terms: (5 + r)(r + 5) = 11 Reorder the terms: (5 + r)(5 + r) = 11 Multiply (5 + r) * (5 + r) (5(5 + r) + r(5 + r)) = 11 ((5 * 5 + r * 5) + r(5 + r)) = 11 ((25 + 5r) + r(5 + r)) = 11 (25 + 5r + (5 * r + r * r)) = 11 (25 + 5r + (5r + r2)) = 11 Combine like terms: 5r + 5r = 10r (25 + 10r + r2) = 11 Solving 25 + 10r + r2 = 11 Solving for variable 'r'. Reorder the terms: 25 + -11 + 10r + r2 = 11 + -11 Combine like terms: 25 + -11 = 14 14 + 10r + r2 = 11 + -11 Combine like terms: 11 + -11 = 0 14 + 10r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 10r + -14 + r2 = 0 + -14 Reorder the terms: 14 + -14 + 10r + r2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 10r + r2 = 0 + -14 10r + r2 = 0 + -14 Combine like terms: 0 + -14 = -14 10r + r2 = -14 The r term is 10r. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10r + 25 + r2 = -14 + 25 Reorder the terms: 25 + 10r + r2 = -14 + 25 Combine like terms: -14 + 25 = 11 25 + 10r + r2 = 11 Factor a perfect square on the left side: (r + 5)(r + 5) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (r + 5) equal to 3.31662479 and -3.31662479.Subproblem 1
r + 5 = 3.31662479 Simplifying r + 5 = 3.31662479 Reorder the terms: 5 + r = 3.31662479 Solving 5 + r = 3.31662479 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = 3.31662479 + -5 Combine like terms: 5 + -5 = 0 0 + r = 3.31662479 + -5 r = 3.31662479 + -5 Combine like terms: 3.31662479 + -5 = -1.68337521 r = -1.68337521 Simplifying r = -1.68337521Subproblem 2
r + 5 = -3.31662479 Simplifying r + 5 = -3.31662479 Reorder the terms: 5 + r = -3.31662479 Solving 5 + r = -3.31662479 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = -3.31662479 + -5 Combine like terms: 5 + -5 = 0 0 + r = -3.31662479 + -5 r = -3.31662479 + -5 Combine like terms: -3.31662479 + -5 = -8.31662479 r = -8.31662479 Simplifying r = -8.31662479Solution
The solution to the problem is based on the solutions from the subproblems. r = {-1.68337521, -8.31662479}
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